Suspend and Resume were (or used to be) potentially broken in the TThread class (if you look at the source you will see that the Suspend method directly and unconditionally sets a Boolean to indicated thread suspended state rather than more robustly deriving this state from the execution count on the thread handle. Ironically the Resume method does use this more robust indicator to update the suspended state Boolean).
This is possibly why they have been deprecated. It's also why I implemented my own class to encapsulate a Windows thread with a more robust suspend and resume mechanism as well as the ability to Restart a thread once it had completed.
I'm not sure why their deprecation is supposedly related to synchronization. Suspending and resuming threads is not necessarily related to synchronization, although I can see how it might be. It's interesting to note that the equivalent methods in the .NET framework Thread class are similarly marked as obsoleted. And the same comments w.r.t synchronization appear in the Windows API documentation for thread suspend/resume.
If using deprecated methods makes you nervous and you still wish to suspend/resume you could always use the Windows API to suspend and resume the thread by reference to it's handle.